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Weak Factorization of Hardy Spaces in the Bessel Setting
We provide the weak factorization of the Hardy spaces H p (ℝ + , dm λ ) in the Bessel setting, for p ∈ ( 2 λ + 1 2 λ + 2 , 1 ] . As a corollary we obtain a characterization of the boundedness of the commutator [ b , R Δ λ ] from L q (ℝ + , dm λ ) to L r (ℝ + , dm λ ) when b ∈ Lip α (ℝ + , dm λ ) pro...
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| Published in: | Analysis mathematica (Budapest) 2019-06, Vol.45 (2), p.391-411 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| container_end_page | 411 |
| container_issue | 2 |
| container_start_page | 391 |
| container_title | Analysis mathematica (Budapest) |
| container_volume | 45 |
| creator | Oliver, R. Wick, B. D. |
| description | We provide the weak factorization of the Hardy spaces
H
p
(ℝ
+
,
dm
λ
) in the Bessel setting, for
p
∈
(
2
λ
+
1
2
λ
+
2
,
1
]
. As a corollary we obtain a characterization of the boundedness of the commutator [
b
,
R
Δ
λ
] from
L
q
(ℝ
+
,
dm
λ
) to
L
r
(ℝ
+
,
dm
λ
) when
b
∈ Lip
α
(ℝ
+
,
dm
λ
) provided that
α
=
1
q
−
1
r
. The results are an adaptation and modification of the work of Duong, Li, Yang, and the second named author, which only considered the case of
p
= 1, which in turn are based on modifications and adaptations of work by Uchiyama. |
| doi_str_mv | 10.1007/s10476-018-0610-5 |
| format | article |
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H
p
(ℝ
+
,
dm
λ
) in the Bessel setting, for
p
∈
(
2
λ
+
1
2
λ
+
2
,
1
]
. As a corollary we obtain a characterization of the boundedness of the commutator [
b
,
R
Δ
λ
] from
L
q
(ℝ
+
,
dm
λ
) to
L
r
(ℝ
+
,
dm
λ
) when
b
∈ Lip
α
(ℝ
+
,
dm
λ
) provided that
α
=
1
q
−
1
r
. The results are an adaptation and modification of the work of Duong, Li, Yang, and the second named author, which only considered the case of
p
= 1, which in turn are based on modifications and adaptations of work by Uchiyama.</description><identifier>ISSN: 0133-3852</identifier><identifier>EISSN: 1588-273X</identifier><identifier>DOI: 10.1007/s10476-018-0610-5</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Commutators ; Factorization ; Mathematics ; Mathematics and Statistics</subject><ispartof>Analysis mathematica (Budapest), 2019-06, Vol.45 (2), p.391-411</ispartof><rights>Akadémiai Kiadó, Budapest 2018</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-af792885be04ae99c64110dec70b760971b046b4f3ebcf615c0a4e9409f1e9ec3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Oliver, R.</creatorcontrib><creatorcontrib>Wick, B. D.</creatorcontrib><title>Weak Factorization of Hardy Spaces in the Bessel Setting</title><title>Analysis mathematica (Budapest)</title><addtitle>Anal Math</addtitle><description>We provide the weak factorization of the Hardy spaces
H
p
(ℝ
+
,
dm
λ
) in the Bessel setting, for
p
∈
(
2
λ
+
1
2
λ
+
2
,
1
]
. As a corollary we obtain a characterization of the boundedness of the commutator [
b
,
R
Δ
λ
] from
L
q
(ℝ
+
,
dm
λ
) to
L
r
(ℝ
+
,
dm
λ
) when
b
∈ Lip
α
(ℝ
+
,
dm
λ
) provided that
α
=
1
q
−
1
r
. The results are an adaptation and modification of the work of Duong, Li, Yang, and the second named author, which only considered the case of
p
= 1, which in turn are based on modifications and adaptations of work by Uchiyama.</description><subject>Analysis</subject><subject>Commutators</subject><subject>Factorization</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0133-3852</issn><issn>1588-273X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kD9PwzAQRy0EEqXwAdgsMRvunMR_RqgoRarEUBBsluNeSkpJip0O5dOTKkhMTLe89zvpMXaJcI0A-iYh5FoJQCNAIYjiiI2wMEZInb0dsxFglonMFPKUnaW0BgCrTDZi5pX8B5_60LWx_vZd3Ta8rfjMx-WeL7Y-UOJ1w7t34neUEm34grqublbn7KTym0QXv3fMXqb3z5OZmD89PE5u5yJIZTrhK22lMUVJkHuyNqgcEZYUNJRagdVYQq7KvMqoDJXCIoDPyeZgKyRLIRuzq2F3G9uvHaXOrdtdbPqXTkpZSASNuqdwoEJsU4pUuW2sP33cOwR3COSGQK4P5A6BXNE7cnBSzzYrin_L_0s_N09m7Q</recordid><startdate>20190601</startdate><enddate>20190601</enddate><creator>Oliver, R.</creator><creator>Wick, B. D.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190601</creationdate><title>Weak Factorization of Hardy Spaces in the Bessel Setting</title><author>Oliver, R. ; Wick, B. D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-af792885be04ae99c64110dec70b760971b046b4f3ebcf615c0a4e9409f1e9ec3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Analysis</topic><topic>Commutators</topic><topic>Factorization</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Oliver, R.</creatorcontrib><creatorcontrib>Wick, B. D.</creatorcontrib><collection>CrossRef</collection><jtitle>Analysis mathematica (Budapest)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Oliver, R.</au><au>Wick, B. D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Weak Factorization of Hardy Spaces in the Bessel Setting</atitle><jtitle>Analysis mathematica (Budapest)</jtitle><stitle>Anal Math</stitle><date>2019-06-01</date><risdate>2019</risdate><volume>45</volume><issue>2</issue><spage>391</spage><epage>411</epage><pages>391-411</pages><issn>0133-3852</issn><eissn>1588-273X</eissn><abstract>We provide the weak factorization of the Hardy spaces
H
p
(ℝ
+
,
dm
λ
) in the Bessel setting, for
p
∈
(
2
λ
+
1
2
λ
+
2
,
1
]
. As a corollary we obtain a characterization of the boundedness of the commutator [
b
,
R
Δ
λ
] from
L
q
(ℝ
+
,
dm
λ
) to
L
r
(ℝ
+
,
dm
λ
) when
b
∈ Lip
α
(ℝ
+
,
dm
λ
) provided that
α
=
1
q
−
1
r
. The results are an adaptation and modification of the work of Duong, Li, Yang, and the second named author, which only considered the case of
p
= 1, which in turn are based on modifications and adaptations of work by Uchiyama.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s10476-018-0610-5</doi><tpages>21</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0133-3852 |
| ispartof | Analysis mathematica (Budapest), 2019-06, Vol.45 (2), p.391-411 |
| issn | 0133-3852 1588-273X |
| language | eng |
| recordid | cdi_proquest_journals_2225210717 |
| source | Springer Nature |
| subjects | Analysis Commutators Factorization Mathematics Mathematics and Statistics |
| title | Weak Factorization of Hardy Spaces in the Bessel Setting |
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